In this paper, we present the Green's functions of closed form for a steady state heat source in a semi-infinite transversely isotropic thermoelastic solid when the functions are expressed as the Cartesian coordinates. For thermal boundary conditions, both cases of the adiabatic condition and/or the zero temperature prescribed on the boundary plane are treated, and for the stress and the displacement boundary conditions the following three cases are treated : (1) the stress free condition on the boundary plane, (2) the fixed displacement condition on the boundary plane and (3) only the displacement uz in the direction z vanishes on the boundary plane. To obtain the solutions of the problem the mirror reflection method is developed by using the solution of the infinite transversely isotropic thermoelastic solid reported in the previous paper. Furthermore, the closed form solutions in a semi-infinite isotropic thermoelastic solid are also shown. Finally, the numerical results for titanium in both cases of isotropy and transverse isotropy are given.